Computational Mathematics and Mathematical Physics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 19052

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Guest Editor
International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy
Interests: continuum mechanics; porous media; piezo-electro-mechanical structures; nonlinear elasticity; second gradient materials; metamaterials; mechanics of living tissue; smart materials; composite materials; experimental mechanics; numerical mechanics
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1. Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Interests: partial differential equations & mathematical physics; elasticity system; stokes system; biharmonic (polyharmonic) equation
Special Issues, Collections and Topics in MDPI journals

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Dipartimento di Scienze Matematiche e Informatiche, scienze Fisiche e Scienze della Terra dell'Università degli Studi di Messina Viale Ferdinando Stagno d'Alcontres, 31-98166 Messina, Italy
Interests: general topology; fibrewise topology; digital geometry; soft topology; neutrosophic topology

Special Issue Information

Dear Colleagues,

The main topics of this Special Issue are:

  • Discrete and Continuum Mechanics
    Metamaterials and smart structure designs, variational methods in mechanics, biomechanics, and experimental mechanics
  • Mathematical Physics and PDE
    Mathematical physics and PDE including fluid dynamics and the Helmhotz equation; solvability, regularity, stability, and other qualitative properties of linear and nonlinear equations and systems; scattering theory and inverse problems; variational methods and calculus of variations; dynamical systems
  • Topology, Computer Science, Digital and Computational Geometry, Soft and Fuzzy Sets
  • Foundations of Mechanics, Postulations of Continuum Mechanics, and Variational Principles

Prof. Dr. Francesco dell’Isola
Prof. Dr. Hovik Matevossian
Prof. Dr. Giorgio Nordo
Guest Editors

Manuscript Submission Information

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Keywords

  • discrete and continuum mechanics, metamaterials and smart structure design
  • variational methods in mechanics, biomechanics, and experimental mechanics
  • mathematical physics and fluid dynamics
  • PDE and applied mathematics
  • general and fiberwise general topology, digital geometry, soft topology, and neutrosophic topology

Published Papers (17 papers)

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Editorial

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6 pages, 215 KiB  
Editorial
“Computational Mathematics and Mathematical Physics”—Editorial I (2021–2023)
by Hovik A. Matevossian and Francesco dell’Isola
Axioms 2023, 12(9), 824; https://doi.org/10.3390/axioms12090824 - 28 Aug 2023
Viewed by 652
Abstract
Based on the papers published in the Special Issue of the scientific journal Axioms, here we present the Editorial Article “Computational Mathematics and Mathematical Physics”, the main topics of which include both fundamental and applied research in computational mathematics and differential equations [...] Read more.
Based on the papers published in the Special Issue of the scientific journal Axioms, here we present the Editorial Article “Computational Mathematics and Mathematical Physics”, the main topics of which include both fundamental and applied research in computational mathematics and differential equations of mathematical physics [...] Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)

Research

Jump to: Editorial

20 pages, 3619 KiB  
Article
Drift Velocity with Elastic Scattering
by Rachel M. Morin and Nicholas A. Mecholsky
Axioms 2023, 12(12), 1076; https://doi.org/10.3390/axioms12121076 - 24 Nov 2023
Viewed by 777
Abstract
The drift velocity of a particle under a driving force has its roots in the theory of electrical conduction. Although it has been studied for over 100 years, it still yields surprises. At the heart of a particle’s drift velocity is an interplay [...] Read more.
The drift velocity of a particle under a driving force has its roots in the theory of electrical conduction. Although it has been studied for over 100 years, it still yields surprises. At the heart of a particle’s drift velocity is an interplay of classical, quantum, and statistical mechanics. Irreversibility and energy loss have been assumed as essential features of drift velocities and very little effort has been made to isolate the aspects of particle transport that are due to elastic mechanisms alone. In this paper, we remove energy loss and quantum mechanics to investigate the classical and statistical factors that can produce a drift velocity using only elastic scattering. A Monte Carlo simulation is used to model a particle in a uniform force field, subject to randomly placed scatterers. Time-, space-, and energy-dependent scattering models, with varied ranges of scattering angles, are investigated. A constant drift velocity is achieved with the time scattering model, which has a constant average time between scattering events. A decreasing drift velocity is observed for space and energy-dependent models. The arrival of a constant drift velocity has to do with a balance of momentum gained between collisions and momentum lost after a collision. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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14 pages, 398 KiB  
Article
Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic Fields
by Vladimir V. Kassandrov, Joseph A. Rizcallah and Ivan A. Matveev
Axioms 2023, 12(11), 1061; https://doi.org/10.3390/axioms12111061 - 20 Nov 2023
Viewed by 740
Abstract
We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (B) in particular. We demonstrate that any B-differentiable function gives rise to a null shear-free congruence (NSFC) on the B-vector space CM and [...] Read more.
We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (B) in particular. We demonstrate that any B-differentiable function gives rise to a null shear-free congruence (NSFC) on the B-vector space CM and on its Minkowski subspace M. Making use of the Kerr–Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of B-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in CM. Any singular point, caustic of an NSFC, is located on the complex null cone of a point on the generating string. Further we describe symmetries and associated gauge and spinor fields, with two electromagnetic types among them. A number of familiar and novel examples of NSFC and their singular loci are described. Finally, we describe a conservative algebraic dynamics of a set of identical particles on the “Unique Worldline” and discuss the connections of the theory with the Feynman–Wheeler concept of “One-Electron Universe”. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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13 pages, 326 KiB  
Article
Quantum Chromodynamics and the Hyperbolic Unitary Group SUh(3)
by Nikolay Popov and Ivan Matveev
Axioms 2023, 12(11), 1058; https://doi.org/10.3390/axioms12111058 - 18 Nov 2023
Viewed by 696
Abstract
The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group SUh(3), which is a symmetry group for the three-dimensional complex space of the [...] Read more.
The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group SUh(3), which is a symmetry group for the three-dimensional complex space of the hyperbolic type. Such an approach allows researchers to discover a profound connection between conserved color charges of the quarks and the symmetries of the hyperbolic three-dimensional complex space. Further, it allows a correct introduction of the Hermitian operators to describe the eight gluons, which are carriers of strong interactions. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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15 pages, 352 KiB  
Article
Congruence Representations via Soft Ideals in Soft Topological Spaces
by Zanyar A. Ameen and Mesfer H. Alqahtani
Axioms 2023, 12(11), 1015; https://doi.org/10.3390/axioms12111015 - 28 Oct 2023
Cited by 5 | Viewed by 760
Abstract
This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense [...] Read more.
This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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9 pages, 278 KiB  
Article
Noninertial Proper Motions of the Minkowski Metric, the Sagnac Effect, and the Twin Paradox
by Nikolay Popov and Ivan Matveev
Axioms 2023, 12(6), 537; https://doi.org/10.3390/axioms12060537 - 30 May 2023
Viewed by 732
Abstract
The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established [...] Read more.
The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established only for the inertial frames of reference, whereas the Sagnac experiment and the twin paradox exist in a noninertial one. We introduce an additional group of motions related to the rotation with uniform angular speed and show that these transformations leave the Minkowski metric invariant. Thus, we can give a firm mathematical ground to a usual easy consideration of the Sagnac effect. It should be noted that the presented result is true for a special case of motions; general coordinate transformations into accelerating frames of reference do not preserve the metric. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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22 pages, 829 KiB  
Article
Existence and Qualitative Properties of Solution for a Class of Nonlinear Wave Equations with Delay Term and Variable-Exponents Nonlinearities
by Mohamed Karek, Sadok Otmani, Keltoum Bouhali, Khaled Zennir, Hatim M. Elkhair, Eltegani I. Hassan, Alnadhief H. A. Alfedeel and Almonther Alarfaj
Axioms 2023, 12(5), 444; https://doi.org/10.3390/axioms12050444 - 30 Apr 2023
Viewed by 840
Abstract
This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy [...] Read more.
This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy method combined with the Faedo–Galerkin method, the local and global existence of solutions are established. Then, the stability estimate of the solution is obtained by introducing a suitable Lyapunov function. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
19 pages, 4746 KiB  
Article
Numerical Computation of Hybrid Morphologies of Nanoparticles on the Dynamic of Nanofluid: The Case of Blood-Based Fluid
by Meznah M. Alanazi, Awatif A. Hendi, Qadeer Raza, Muhammad Abdul Rehman, Muhammad Zubair Akbar Qureshi, Bagh Ali and Nehad Ali Shah
Axioms 2023, 12(2), 163; https://doi.org/10.3390/axioms12020163 - 06 Feb 2023
Cited by 13 | Viewed by 1373
Abstract
The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of [...] Read more.
The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of biological fluids flows with the effect of TiO2 and Ag hybrid nanoparticles was developed. Further, we explain the engineering phenomena of biological fluids and the role of hybrid nanoparticles in the blood vessel system. The improvement of drug delivery systems by using low seepage Reynolds number was associated with expansion/contraction and was discussed in detail through the rectangular domain. Using similarity transformation, the governing equations were converted into non-linear ordinary differential equations, and the mathematical problem was solved by employing the numerical shooting method. Plots of momentum, temperature, skin friction coefficient, as well as the Nusselt number on different non-dimensionless parameters are displayed via lower/upper porous walls of the channel. It was analyzed that the walls of the channel showed different results on magnetized physical parameters. Values of thermophoresis and the Brownian motion flow of the heat transfer rate gradually increased on the upper wall and decreased on the lower wall of the channel. The important thing is that the hybrid nanoparticles, rather than nano, were more useful for improving thermal conductivity, heat transfer rate, and the nano-layer. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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12 pages, 780 KiB  
Article
Particles Dynamics in Schwarzschild like Black Hole with Time Contracting Horizon
by Muhammad Atif Khan, Farhad Ali, Nahid Fatima and Mohamed Abd El-Moneam
Axioms 2023, 12(1), 34; https://doi.org/10.3390/axioms12010034 - 27 Dec 2022
Cited by 1 | Viewed by 1109
Abstract
The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy [...] Read more.
The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy of black holes reduce continuously with the passage of time t. For this reason the metric tensor of the black hole should depends on time t. In this work, a time-dependent term is introduced in the horizon of black hole without losing its symmetry structure by using the approximate Noether symmetry equation. The time-dependent term affects the effective potential, effective force, and all the dynamic features of the black hole. They are discussed for neutral and charged particles. Profiles of the escape velocity of colliding particles are also taken into consideration. Lyapunov exponent is used to check the stability of the orbits of the black hole. Hawking temperature, Bekenstein entropy, Komar energy, and specific energy at horizon of the black hole are discussed in this scenario. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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24 pages, 5529 KiB  
Article
Tandem Recurrence Relations for Coefficients of Logarithmic Frobenius Series Solutions about Regular Singular Points
by Ramses van der Toorn
Axioms 2023, 12(1), 32; https://doi.org/10.3390/axioms12010032 - 27 Dec 2022
Viewed by 1262
Abstract
We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this [...] Read more.
We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel’s equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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14 pages, 334 KiB  
Article
Six-Dimensional Space with Symmetric Signature and Some Properties of Elementary Particles
by Nikolay Popov and Ivan Matveev
Axioms 2022, 11(11), 650; https://doi.org/10.3390/axioms11110650 - 17 Nov 2022
Cited by 2 | Viewed by 1400
Abstract
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, [...] Read more.
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, and hypercharge, are expressed through the symmetries of this space. The symmetries are brought out by the various representation of the metric in E3,3 with the aid of spinors and hyperbolic complex numbers. The properties of the metric allow predicting the number of quarks equal to 18. The violation of strong conservation laws in weak interactions is treated through compactifying the three-dimensional temporal subspace at the subparticle scale into single-dimensional time at bigger scales, which reduces symmetry from the spherical to axial type. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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13 pages, 287 KiB  
Article
Global Existence of Bounded Solutions for Eyring–Powell Flow in a Semi-Infinite Rectangular Conduct
by Saeed ur Rahman, Jose Luis Diaz Palencia, Nomaq Tariq, Pablo Salgado Sánchez and Julian Roa Gonzalez
Axioms 2022, 11(11), 625; https://doi.org/10.3390/axioms11110625 - 08 Nov 2022
Cited by 2 | Viewed by 926
Abstract
The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial [...] Read more.
The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial velocity profiles (u10,u20) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u10,u20)L2(Ω), Ω=[0,L]×[0,H]×(0,). Afterward, the results are extended for (u10,u20)Lp(Ω)p>2. Lastly, the existence criteria are obtained when (u10,u20)H1(Ω). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
6 pages, 228 KiB  
Article
A Valid Quantization of the Particle in a Box Field Theory, and Well Beyond
by John R. Klauder
Axioms 2022, 11(10), 567; https://doi.org/10.3390/axioms11100567 - 19 Oct 2022
Viewed by 916
Abstract
The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The result leads to a valid affine quantization of the particle in a box field theory, which points toward further valid [...] Read more.
The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The result leads to a valid affine quantization of the particle in a box field theory, which points toward further valid quantizations of more realistic field theory models. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
17 pages, 386 KiB  
Article
Goodness-of-Fit Tests for Weighted Generalized Quasi-Lindley Distribution Using SRS and RSS with Applications to Real Data
by SidAhmed Benchiha, Amer Ibrahim Al-Omari and Ghadah Alomani
Axioms 2022, 11(10), 490; https://doi.org/10.3390/axioms11100490 - 21 Sep 2022
Cited by 1 | Viewed by 1039
Abstract
This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include [...] Read more.
This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback–Leibler, Kolomogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs’ power increases. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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13 pages, 307 KiB  
Article
Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients II
by Hovik A. Matevossian, Maria V. Korovina and Vladimir A. Vestyak
Axioms 2022, 11(9), 473; https://doi.org/10.3390/axioms11090473 - 16 Sep 2022
Cited by 4 | Viewed by 1178
Abstract
The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients [...] Read more.
The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients for large values of the time parameter t. To obtain this asymptotic expansion as t→∞, methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of a non-positive Hill operator with periodic coefficients. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
22 pages, 2046 KiB  
Article
Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species
by Qimei Zhou, Fengde Chen and Sijia Lin
Axioms 2022, 11(8), 365; https://doi.org/10.3390/axioms11080365 - 26 Jul 2022
Cited by 8 | Viewed by 1270
Abstract
Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of [...] Read more.
Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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5 pages, 221 KiB  
Article
A Valid Quantization of a Half-Harmonic Oscillator Field Theory
by John R. Klauder
Axioms 2022, 11(8), 360; https://doi.org/10.3390/axioms11080360 - 24 Jul 2022
Cited by 1 | Viewed by 1123
Abstract
The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of [...] Read more.
The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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